What are the numerical measures of each angle in the diagram?

29 degrees

151 degrees  

Step-by-step explanation:

m∠1 = 29° = m∠3

m∠2 = 151° = m∠4  

Step-by-step explanation:

m∠1 = (3x -1)° and m∠3 = (2x + 9)°

Since, ∠1 and ∠2 are vertically opposite angles and we know that vertically opposite angles are always equal

⇒ ∠1 = ∠2

⇒ (3x -1)° = (2x + 9)°

⇒ 3x - 2x = 9 + 1

⇒ x = 10

⇒ m∠1 = 3 × 10 - 1

⇒ m∠1 = 29° = m∠3

Now, m∠2 + m∠3 = 180° ( sum of linear pair is 180° )

⇒ m∠2 = 180° - 29°

⇒ m∠2 = 151°

Also, ∠2 = ∠4 ( Vertically opposite angles are always equal)

⇒ m∠2 = 151° = m∠4

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1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages